Open review queue

The grade rests on the announcing lab alone.

Better evidenced, still unconfirmed outside the lab.

The year the problem was first posed.

Finite-time blowup for the unforced Euler equations from smooth compactly supported data Disputed claim that Catalan's constant is irrational Randomized metric distortion improved to 2.3282 Lean proof that the percolation probability vanishes at the critical point in every dimension Hyperbolic surfaces with large systoles in every large genus Not every Heyting algebra is the subterminal lattice of a topos Supporting affine functionals for entanglement of formation need not exist Counterexample to Nevanlinna's half-plane omitted-values question Improved algebraic construction for off-diagonal Ramsey numbers Elliptic curves over the rationals of rank at least 30 and at least 31 A smooth random fast dynamo on the three-torus Bounded prime gaps of 246 formalized in Lean from Bombieri-Vinogradov Complete minimizer picture for Gamow's liquid drop model A prescribed Hamiltonian cycle that a book-embedding algorithm cannot produce Proportion of zeta zeros on the critical line raised to 67.25% Optimal exponent relating sumsets and difference sets determined Sabidussi's compatibility conjecture proved Counterexample to Grothendieck's question on finite flat group schemes First Herculaneum scroll read end to end without unrolling it Two kagome superconductors predicted by machine learning and confirmed in the lab Nine Erdős problems and 44 OEIS conjectures proved with machine-checked proofs Phase 1 trial of a computationally designed pan-sarbecovirus vaccine An antibiotic designed by reinforcement learning clears an MRSA infection in mice Structure in Bruhat intervals of permutation groups Erdős problem #728 resolved and formalized in Lean Early science acceleration experiments with GPT-5 AlphaEvolve across 67 problems: 20 improvements, 8 regressions GPT-5 "solved 10 Erdős problems": it located existing solutions Limits to black-box amplification in QMA, with the key step written by GPT-5 New families of unstable singularities in fluid equations AI-generated bacteriophage genomes that replicate and kill bacteria Strong prime number theorem formalized in Lean by an autoformalization agent Improved step-size bound in smooth convex optimization Machine-checked Lean proofs for five of six 2025 IMO problems Gold-medal standard at the 2025 International Mathematical Olympiad Phase 2a results for a drug whose target and molecule both came from AI Candidate treatment for dry age-related macular degeneration A fully machine-generated paper passed workshop peer review AI co-scientist hypotheses on antimicrobial resistance and liver fibrosis Enzymes with working catalytic machinery designed from scratch A working fluorescent protein generated by a language model Generative model designs crystals to order; its flagship synthesis turned out to be a known compound A neural decoder that identifies quantum errors more accurately than hand-designed methods Complete wiring diagram of an adult fruit-fly brain Silver-medal standard at the 2024 International Mathematical Olympiad Joint structure prediction for proteins, nucleic acids and ligands (AlphaFold 3) Reinforcement learning steers a tokamak away from tearing instabilities Olympiad geometry solved without human demonstrations A language-model agent that planned and ran chemistry experiments on lab robots A new structural class of antibiotic candidates against MRSA Large-scale prediction of new stable crystalline materials (GNoME) Autonomous laboratory reports solid-state synthesis of new inorganic compounds Medium-range weather forecasts from a graph neural network beat the operational physics model Pathogenicity predictions for 71 million human missense variants Faster sorting routines discovered and merged into the LLVM C++ library Deep reinforcement learning controls tokamak fusion plasma Two theorems found by machine pattern-spotting in knot theory and representation theory Reinforcement learning refutes several conjectures in extremal combinatorics Halicin, an antibiotic found by a neural network screening a compound library An eighth planet around Kepler-90 found by a neural network

A thread where the result was debated.

Finite-time blowup for Navier-Stokes with smooth forcing, Clay alternatives C and D Finite-time blowup for the unforced Euler equations from smooth compactly supported data Fermat's Last Theorem formalized end to end in Lean 4 Lean disproof of Krempa's matrix form of the Koethe conjecture Erdos-Sos conjecture proved in Lean, in a form marginally weaker than the classical statement Disputed claim that Catalan's constant is irrational A quantum oracle separating QMA(2) from QMA Confirmation of the Daykin-Frankl conjecture from a language-model proof A smooth counterexample to the Trautman conjecture Entropy production of the Boltzmann equation is not always monotone Common neighbour conjectures for Saxl graphs fail at every base size Counterexample to the stable forking conjecture Unrestricted Boolean multiplicative complexity of four-term binary polynomial multiplication Criteria and two quadratic instances for Bugeaud's Problem 10.61 Dean's conjecture for k = 5, cycles of length divisible by five Randomized metric distortion improved to 2.3282 Lean proof that the percolation probability vanishes at the critical point in every dimension Hyperbolic surfaces with large systoles in every large genus Not every Heyting algebra is the subterminal lattice of a topos Supporting affine functionals for entanglement of formation need not exist Counterexample to Nevanlinna's half-plane omitted-values question Rapid mixing for spin systems on graphs of girth at least five Improved algebraic construction for off-diagonal Ramsey numbers Improved lower bound for large gaps between consecutive primes Sparse domination implies convex body domination Equivalence of generic stability notions for Keisler measures Fröberg's conjecture for quintics and septics in four variables Optimal linear encoding rate for lossy compression of Bernoulli sources A proposed complex structure on the six-sphere Elliptic curves over the rationals of rank at least 30 and at least 31 Transcendence in the affine case of Erdős Problem 270 Dubickas's question on integral parts of powers of square roots settled Stable commutator length of a relator is not a one-relator group invariant Counterexample to the bounded mass property on the Hopf threefold Marton's inner bound shown not to reach the broadcast channel capacity region A smooth random fast dynamo on the three-torus Counterexamples to the fractional colouring conjecture for Pauli shadow tomography Counterexample to the Yau–Tian–Donaldson conjecture for constant scalar curvature metrics Counterexample to the smooth Carathéodory conjecture on umbilic points First open case of the big-line-big-clique conjecture Counting linear extensions below the 2^n barrier Erdős Problem #501 shown independent of ZFC, with both directions in Lean The DeLaViña-Waller conjecture on the Wiener index Partial proof of the Kasami APN triple-count conjecture, verified in Lean Bounded prime gaps of 246 formalized in Lean from Bombieri-Vinogradov Dimension-free weak-type bound for the vector Riesz transform Matrix multiplication exponent lowered to below 2.371177 Talagrand's convolution conjecture proved on the Boolean hypercube SOP_2 and SOP_3 theories shown to coincide Banach's isometric conjecture settled in the remaining odd dimensions Complete minimizer picture for Gamow's liquid drop model A prescribed Hamiltonian cycle that a book-embedding algorithm cannot produce Proportion of zeta zeros on the critical line raised to 67.25% A 112-vertex counterexample to the Petersen coloring conjecture Separation between the ordinary and strong Kreiss constants Sendov's conjecture proved for every degree Counterexamples to Schiffer's conjecture and the Pompeiu problem Asymptotic degree-diameter problem resolved for fixed diameter Ten results in mathematics and theoretical computer science with Lean certificates Optimal exponent relating sumsets and difference sets determined Kemeny rank aggregation shown NP-hard for three voters Feige's conjecture on sums of nonnegative random variables settled Counterexamples to the Gaussian moments conjecture Eight problems from the Kourovka Notebook solved and formalized in Lean Gaussian product inequality conjecture proved Counterexample to the Jacobian conjecture in dimension three Near-quadratic lower bound for derivative-free convex optimization Sabidussi's compatibility conjecture proved Counterexample to Grothendieck's question on finite flat group schemes First Herculaneum scroll read end to end without unrolling it Two kagome superconductors predicted by machine learning and confirmed in the lab Identity for the critical exponents of jamming derived analytically Nine Erdős problems and 44 OEIS conjectures proved with machine-checked proofs Disproof of the Erdős unit-distance conjecture Phase 1 trial of a computationally designed pan-sarbecovirus vaccine An antibiotic designed by reinforcement learning clears an MRSA infection in mice Structure in Bruhat intervals of permutation groups Erdős problem #728 resolved and formalized in Lean Early science acceleration experiments with GPT-5 AlphaEvolve across 67 problems: 20 improvements, 8 regressions Limits to black-box amplification in QMA, with the key step written by GPT-5 New families of unstable singularities in fluid equations AI-generated bacteriophage genomes that replicate and kill bacteria Strong prime number theorem formalized in Lean by an autoformalization agent Machine-checked Lean proofs for five of six 2025 IMO problems Gold-medal standard at the 2025 International Mathematical Olympiad Phase 2a results for a drug whose target and molecule both came from AI Candidate treatment for dry age-related macular degeneration A fully machine-generated paper passed workshop peer review AI co-scientist hypotheses on antimicrobial resistance and liver fibrosis Enzymes with working catalytic machinery designed from scratch A working fluorescent protein generated by a language model Generative model designs crystals to order; its flagship synthesis turned out to be a known compound A neural decoder that identifies quantum errors more accurately than hand-designed methods Complete wiring diagram of an adult fruit-fly brain Joint structure prediction for proteins, nucleic acids and ligands (AlphaFold 3) Reinforcement learning steers a tokamak away from tearing instabilities Olympiad geometry solved without human demonstrations A language-model agent that planned and ran chemistry experiments on lab robots A new structural class of antibiotic candidates against MRSA Medium-range weather forecasts from a graph neural network beat the operational physics model Pathogenicity predictions for 71 million human missense variants Two theorems found by machine pattern-spotting in knot theory and representation theory Accurate protein structure prediction across the known proteome (AlphaFold2) Reinforcement learning refutes several conjectures in extremal combinatorics Halicin, an antibiotic found by a neural network screening a compound library An eighth planet around Kepler-90 found by a neural network

Nobody has cited a rebuttal, a critical review, or prior work. An entry with no challenge is not necessarily unchallenged; it may just be unexamined.

Finite-time blowup for the unforced Euler equations from smooth compactly supported data Fermat's Last Theorem formalized end to end in Lean 4 Lean disproof of Krempa's matrix form of the Koethe conjecture Erdos-Sos conjecture proved in Lean, in a form marginally weaker than the classical statement A quantum oracle separating QMA(2) from QMA Confirmation of the Daykin-Frankl conjecture from a language-model proof A smooth counterexample to the Trautman conjecture Entropy production of the Boltzmann equation is not always monotone Common neighbour conjectures for Saxl graphs fail at every base size Counterexample to the stable forking conjecture Unrestricted Boolean multiplicative complexity of four-term binary polynomial multiplication Criteria and two quadratic instances for Bugeaud's Problem 10.61 Dean's conjecture for k = 5, cycles of length divisible by five Randomized metric distortion improved to 2.3282 Lean proof that the percolation probability vanishes at the critical point in every dimension Hyperbolic surfaces with large systoles in every large genus Not every Heyting algebra is the subterminal lattice of a topos Supporting affine functionals for entanglement of formation need not exist Counterexample to Nevanlinna's half-plane omitted-values question Rapid mixing for spin systems on graphs of girth at least five Improved algebraic construction for off-diagonal Ramsey numbers Improved lower bound for large gaps between consecutive primes Sparse domination implies convex body domination Equivalence of generic stability notions for Keisler measures Fröberg's conjecture for quintics and septics in four variables Optimal linear encoding rate for lossy compression of Bernoulli sources A proposed complex structure on the six-sphere Elliptic curves over the rationals of rank at least 30 and at least 31 Transcendence in the affine case of Erdős Problem 270 Dubickas's question on integral parts of powers of square roots settled Stable commutator length of a relator is not a one-relator group invariant Counterexample to the bounded mass property on the Hopf threefold Marton's inner bound shown not to reach the broadcast channel capacity region A smooth random fast dynamo on the three-torus Counterexamples to the fractional colouring conjecture for Pauli shadow tomography Counterexample to the Yau–Tian–Donaldson conjecture for constant scalar curvature metrics Counterexample to the smooth Carathéodory conjecture on umbilic points First open case of the big-line-big-clique conjecture Counting linear extensions below the 2^n barrier Erdős Problem #501 shown independent of ZFC, with both directions in Lean The DeLaViña-Waller conjecture on the Wiener index Partial proof of the Kasami APN triple-count conjecture, verified in Lean Bounded prime gaps of 246 formalized in Lean from Bombieri-Vinogradov Dimension-free weak-type bound for the vector Riesz transform Matrix multiplication exponent lowered to below 2.371177 Talagrand's convolution conjecture proved on the Boolean hypercube SOP_2 and SOP_3 theories shown to coincide Banach's isometric conjecture settled in the remaining odd dimensions Complete minimizer picture for Gamow's liquid drop model A prescribed Hamiltonian cycle that a book-embedding algorithm cannot produce Proportion of zeta zeros on the critical line raised to 67.25% A 112-vertex counterexample to the Petersen coloring conjecture Separation between the ordinary and strong Kreiss constants Sendov's conjecture proved for every degree Counterexamples to Schiffer's conjecture and the Pompeiu problem Asymptotic degree-diameter problem resolved for fixed diameter Ten results in mathematics and theoretical computer science with Lean certificates Optimal exponent relating sumsets and difference sets determined Kemeny rank aggregation shown NP-hard for three voters Feige's conjecture on sums of nonnegative random variables settled Counterexample to the Dinitz–Garg–Goemans conjecture Counterexamples to the Gaussian moments conjecture Eight problems from the Kourovka Notebook solved and formalized in Lean Gaussian product inequality conjecture proved Counterexample to the Jacobian conjecture in dimension three Near-quadratic lower bound for derivative-free convex optimization Sabidussi's compatibility conjecture proved Counterexample to Grothendieck's question on finite flat group schemes Cycle double cover conjecture proved for all bridgeless multigraphs First Herculaneum scroll read end to end without unrolling it Two kagome superconductors predicted by machine learning and confirmed in the lab Identity for the critical exponents of jamming derived analytically Nine Erdős problems and 44 OEIS conjectures proved with machine-checked proofs Disproof of the Erdős unit-distance conjecture Phase 1 trial of a computationally designed pan-sarbecovirus vaccine An antibiotic designed by reinforcement learning clears an MRSA infection in mice Structure in Bruhat intervals of permutation groups Erdős problem #728 resolved and formalized in Lean Early science acceleration experiments with GPT-5 AlphaEvolve across 67 problems: 20 improvements, 8 regressions Limits to black-box amplification in QMA, with the key step written by GPT-5 New families of unstable singularities in fluid equations AI-generated bacteriophage genomes that replicate and kill bacteria Strong prime number theorem formalized in Lean by an autoformalization agent Machine-checked Lean proofs for five of six 2025 IMO problems Gold-medal standard at the 2025 International Mathematical Olympiad Phase 2a results for a drug whose target and molecule both came from AI 4×4 complex matrix multiplication in 48 scalar multiplications Improved lower bound for the 11-dimensional kissing number Improved bound for the Erdős minimum-overlap problem Candidate treatment for dry age-related macular degeneration AI co-scientist hypotheses on antimicrobial resistance and liver fibrosis Enzymes with working catalytic machinery designed from scratch A working fluorescent protein generated by a language model A neural decoder that identifies quantum errors more accurately than hand-designed methods Complete wiring diagram of an adult fruit-fly brain Silver-medal standard at the 2024 International Mathematical Olympiad Joint structure prediction for proteins, nucleic acids and ligands (AlphaFold 3) Reinforcement learning steers a tokamak away from tearing instabilities Olympiad geometry solved without human demonstrations A language-model agent that planned and ran chemistry experiments on lab robots A new structural class of antibiotic candidates against MRSA New lower bound constructions for the cap set problem Improved heuristics for online bin packing Medium-range weather forecasts from a graph neural network beat the operational physics model Pathogenicity predictions for 71 million human missense variants Faster sorting routines discovered and merged into the LLVM C++ library Faster matrix-multiplication algorithms found by reinforcement learning Deep reinforcement learning controls tokamak fusion plasma Accurate protein structure prediction across the known proteome (AlphaFold2) Halicin, an antibiotic found by a neural network screening a compound library An eighth planet around Kepler-90 found by a neural network